TH Journal Club on String Theory

Gabor Sarosi: "Geometric secret sharing in a model of Hawking radiation"

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We consider a model of microstates of a BTZ black hole in terms of states of a field theory living on an end of the world brane behind the horizon. We take this field theory to have its own holographic dual geometry, which we call the "inception geometry". In this context, we propose a simple model of quantum extremal surfaces as regular RT surfaces in a geometry obtained by gluing the inception geometry (dual to the state of the brane) to the original black hole spacetime along the end of the world brane. We apply this rule to the case when the microstates are entangled with some auxiliary system (modelling Hawking radiation), and explain how the rule produces the Page curve. We then consider splitting the radiation into subsystems and show that there are new extremal surfaces suggesting that in certain cases parts of the interior can be reconstructed from having access to parts of the radiation. While the entanglement wedge of the union of radiation subsystems covers the complete black hole interior at late times, the union of entanglement wedges of the subsystems may not. When this occurs, the interior contains a shared secret, which in our model turns out to be a spatial subregion of the interior.